Problem: The sum of two numbers is $108$, and their difference is $16$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 108}$ ${x-y = 16}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 124 $ $ x = \dfrac{124}{2} $ ${x = 62}$ Now that you know ${x = 62}$ , plug it back into $ {x+y = 108}$ to find $y$ ${(62)}{ + y = 108}$ ${y = 46}$ You can also plug ${x = 62}$ into $ {x-y = 16}$ and get the same answer for $y$ ${(62)}{ - y = 16}$ ${y = 46}$ Therefore, the larger number is $62$, and the smaller number is $46$.